Open Access
November 2015 Derivatives of meromorphic functions and sine function
Pai Yang, Xiaojun Liu, Xuecheng Pang
Proc. Japan Acad. Ser. A Math. Sci. 91(9): 129-134 (November 2015). DOI: 10.3792/pjaa.91.129


In the paper, we take up a new method to prove the following result. Let $f$ be a meromorphic function in the complex plane, all of whose zeros have multiplicity at least $k+1$ ($k\geq 2$) and all of whose poles are multiple. If $T(r,\sin z)=o\{T(r,f(z))\}$ as $n\rightarrow\infty$, then $f^{(k)}(z)-\sin z$ has infinitely many zeros.


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Pai Yang. Xiaojun Liu. Xuecheng Pang. "Derivatives of meromorphic functions and sine function." Proc. Japan Acad. Ser. A Math. Sci. 91 (9) 129 - 134, November 2015.


Published: November 2015
First available in Project Euclid: 29 October 2015

zbMATH: 1337.30045
MathSciNet: MR3418201
Digital Object Identifier: 10.3792/pjaa.91.129

Primary: 30D35 , 30D45

Keywords: meromorphic function , normal familiy , sine function

Rights: Copyright © 2015 The Japan Academy

Vol.91 • No. 9 • November 2015
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